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#include <bits/stdc++.h>
 
#define INF 2147483647
#define LINF 9223372036854775807
#define NINF -2147483648
#define NLINF -9223372036854775808
#define M 1000000007
#define M1 998244353
#define A 26
#define K 31
#define P 2137
 
using namespace std;
using db=double;
using dbl=long double;
using ll=long long;
using pi=pair<int,int>;
using pl=pair<ll,ll>;
using vi=vector<int>;
using vl=vector<ll>;
using gr=vector<vector<int> >;
using grl=vector<vector<ll> >;

 
#define fp(x, a, b) for (int (x) = (a); (x) < (b); (x)++)
#define f(x, n) for (int (x) = 0; (x) < (n); (x)++)
#define fnp(x, a, b) for (int (x) = (b) - 1; (x) >= (a); (x)--)
#define fn(x, n) for (int (x) = (n - 1); (x) >= 0; (x)--)
#define sgn(x) (x) > 0 ? 1 : (x) == 0 ? 0 : -1
#define gcd(a, b) __gcd((a), (b))
#define lcm(a, b) (a) * (b) / gcd((a), (b))
#define x first
#define y second
#define mp make_pair 
#define pb push_back
#define s(x) x.size()
#define all(x) x.begin(), x.end()
#define ans(x) cout<<(x)<<"\n"
#define yes cout<<"YES\n";
#define no cout<<"NO\n";
#define fl cout.flush()
#define debarr(x, n) f(i, (n)){cout<<(x)[i]<<" ";}cout<<"\n"
#define debgr(x, n) f(i, (n)){f(j, s((x)[i])){cout<<(x)[i][j]<<" ";}cout<<"\n";}

 
mt19937 rnd(chrono::high_resolution_clock::now().time_since_epoch().count());


 
void input();
void compute();
 
int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	int T = 1;
	//cin >> T;
	while(T--) {
		input();
		compute();
	}
	return 0;
}

#define N 310
 
int n;
int k;
ll cnt[N][N];
ll dp[N][N][N];
string s;


ll count(int a, int b) {
	ll sum = 0;
	fp(i, a, b) {
		int cSum = 0;
		fp(j, i, b) {
			if(s[j] == '('){
				cSum++;
			} else {
				cSum--;
			}
			if(cSum < 0) {
				break;
			}
			if(cSum == 0) {
				sum++;
			}
		}
	}
	return sum;
}

void input() {
	cin >> n >> k >> s;
}

void compute() {
	if(n == 1) {
		ans(0);
		return;
	}
	if(k == 1) {
		ans(count(0, n));
		return;
	}
	k--;
	f(i, n) {
		fp(j, i + 1, n) {
			cnt[i][j] = count(i, j + 1);
		}
	}
	f(i, n + 1) {
		f(j, i) {
			f(l, i) {
				dp[i][j][l] = INF;
			}
		}
	}
	f(i, n) {
		dp[i][0][0] = 0;
	}
	f(i, n + 1) {
		f(j, i) {
			f(l, j == 0 ? 1 : i) {
				//cout<<i<<" "<<j<<" "<<l<<" "<<dp[i][j][l]<<" "<<dp[i][j][l] + cnt[l][n - 1]<<"\n";
				dp[i + 1][j][l] = min(dp[i + 1][j][l], dp[i][j][l]);
				dp[i + 1][j + 1][i] = min(dp[i + 1][j + 1][i], dp[i][j][l] + cnt[l][i - 1]);
			}
		}
	}
	ll min = INF;
	fp(i, k + 1, n + 1) {
		f(l, i) {
			//cout<<i<<" "<<k<<" "<<l<<" "<<dp[i][k][l]<<" "<<cnt[l][n - 1]<<"h\n";
			dp[i][k][l] += cnt[l][n - 1];
			if(dp[i][k][l] < min) {
				min = dp[i][k][l];
			}
		}
	}
	cout<<min<<"\n";
}